A company policy requires that, for every 50 employees, there must be 3 supervisors. If there are 276 supervisors at the company
2 answers:
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The ODE has an equilibrium point at
We want to be an unstable equilibrium solution - in other words, we want all solutions with initial condition
for
near 2 to diverge from
- so
.
Divergence from would require that for
, any solution is increasing, and for
, and solution is decreasing. In order for that to happen, we need
if , and
if .
Now we just pick to satisfy these conditions. An easy choice is
, which forces
, so that one possible ODE would be
I've attached a plot of the slope field to demonstrate the behavior of the solutions.
The surface area of a sphere is 
and if the original S.A was is enlarged to have it 9 times greater, the radius would be multiplied by 3 or roughly 2.99626 rounded off to 3.0.
For example, let us assign values.
Let A=90
A= 90*9 = 810
and 
the first r is 2.68 and the second r is 8.03
then,
or rounded off to 3.
For example, let us assign values.
Let A=90
A= 90*9 = 810
the first r is 2.68 and the second r is 8.03
then,
I think 1/4 is a good answer?
and
and